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Correlation analysis
- 2. 𝑟𝑝 = Σ𝑑 𝑥 𝑑 𝑦 𝑛𝜎𝑥 𝜎 𝑦 = Σ𝑑 𝑥 𝑑 𝑦 𝑑 𝑥 2 𝑑 𝑦 2 𝑟𝑝 = Σ𝑋𝑌 𝑛 − Σ𝑋 𝑛 Σ𝑌 𝑛 Σ𝑋2 𝑛 − Σ𝑋 𝑛 2 Σ𝑌2 𝑛 − Σ𝑌 𝑛 2 𝑟𝑝 = Σ𝑑 𝑥 𝑑 𝑦 𝑛 − Σ𝑑 𝑥 𝑛 Σ𝑑 𝑦 𝑛 Σ𝑑 𝑥 2 𝑛 − Σ𝑑 𝑥 𝑛 2 Σ𝑑 𝑦 2 𝑛 − Σ𝑑 𝑦 𝑛 2
- 3. 𝐶𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑋, 𝑌 = Σ𝑑 𝑥 𝑑 𝑦 𝑛 𝑟𝑠 = 1 − 6Σ𝑑2 𝑛3 − 𝑛 𝑟𝑠 = 1 − 6 Σ𝑑2 + 1 12 𝑚1 3 − 𝑚1 + 1 12 𝑚2 3 − 𝑚2 + 1 12 𝑚3 3 − 𝑚3 + ⋯ 𝑛3 − 𝑛